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Bark Difference DCT Normalization

Source: R/dct_norm.R
norm_dct_barkz.Rd

Bark Difference DCT Normalization

Usage

norm_dct_barkz(
  .data,
  ...,
  .token_id_col,
  .by = NULL,
  .param_col = NULL,
  .drop_orig = FALSE,
  .names = "{.formant}_bz",
  .silent = FALSE
)

Arguments

.data

A data frame containing vowel formant data

...

<tidy-select> One or more unquoted expressions separated by commas. These should target the vowel formant data columns.

.token_id_col

<data-masking> A column that identifies token ids.

.by

<tidy-select> A selection of columns to group by. Typically a column of speaker IDs.

.param_col

A column identifying the DCT parameter number.

.drop_orig

Should the originally targeted columns be dropped.

.names

A glue::glue() expression for naming the normalized data columns. The "{.formant}" portion corresponds to the name of the original formant columns.

.silent

Whether or not the informational message should be printed.

Value

A data frame of normalized DCT parameters.

A data frame of Back Difference normalized dct coefficients.

Details

Important: This function assumes that the DCT coefficients were estimated over bark-transformed formant values.

This is a within-token normalization technique. First all formants are converted to Bark (see hz_to_bark), then, within each token, F3 is subtracted from F1 and F2.

$$ \hat{F}_{ij} = F_{ij} - L_j $$

$$ L_j = F_{3j} $$

References

Syrdal, A. K., & Gopal, H. S. (1986). A perceptual model of vowel recognition based on the auditory representation of American English vowels. The Journal of the Acoustical Society of America, 79(4), 1086–1100. doi:10.1121/1.393381

Examples

library(tidynorm)
library(dplyr)
#> 
#> Attaching package: ‘dplyr’
#> The following objects are masked from ‘package:stats’:
#> 
#>     filter, lag
#> The following objects are masked from ‘package:base’:
#> 
#>     intersect, setdiff, setequal, union
ggplot2_inst <- require(ggplot2)

speaker_dct <- speaker_tracks |>
  mutate(
    across(F1:F3, hz_to_bark)
  ) |>
  reframe_with_dct(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .time_col = t
  )

# Normalize DCT coefficients
speaker_dct_norm <- speaker_dct |>
  norm_dct_barkz(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .param_col = .param
  )
#> Normalization info
#> • normalized with `tidynorm::norm_dct_barkz()`
#> • normalized `F1`, `F2`, and `F3`
#> • normalized values in `F1_bz`, `F2_bz`, and `F3_bz`
#> • token id column: `id`
#> • DCT parameter column: `.param`
#> • grouped by `speaker`
#> • within formant: FALSE
#> • within token: TRUE
#> • (.formant - .formant[3])/(1/sqrt(2))
#> 

# Apply average and apply inverse dct
# to plot tracks
track_norm_means <- speaker_dct_norm |>
  summarise(
    .by = c(speaker, vowel, .param),
    across(
      ends_with("_bz"),
      mean
    )
  ) |>
  reframe_with_idct(
    ends_with("_bz"),
    .by = speaker,
    .token_id_col = vowel,
    .param_col = .param
  )


if (ggplot2_inst) {
  track_norm_means |>
    ggplot(
      aes(F2_bz, F1_bz, color = speaker)
    ) +
    geom_path(
      aes(
        group = interaction(speaker, vowel)
      )
    ) +
    scale_x_reverse() +
    scale_y_reverse() +
    scale_color_brewer(palette = "Dark2") +
    coord_fixed()
}